1. Field of the Invention
The present invention relates to a position detector; position detecting method, computer program, and a storage medium storing the computer program that are capable of determining error in each positional information of a movable body which is detected time sequentially, and that are capable of removing, correcting, or complementing the positional information including the error, and relates to a data determination apparatus, data determination method and a computer program that are capable of determining the error not only in the time-sequential positional information but also in each data representing an observed value of sequential variables.
2. Description of Related Art
In recent years, it is known a service that parents are capable of recognizing the present position and the moving locus of their child by having the child carry a cell phone provided with a global positioning system (GPS) function, in order to prevent crimes or to address happened problems easily. Similarly, it is known a service capable of recognizing the present position and the moving locus of a vehicle such as an automobile by having the vehicle provided with a GPS terminal apparatus, in order to address theft.
In the aforementioned services, the GPS terminal apparatus receives time information from GPS satellites, measures a distance from the GPS satellites on the basis of a deviation of the time information and detects own position. Further, in some cases, a position is roughly detected or the detected position is corrected by receiving positional information or correcting information from a base station. The positional information detected by the GPS terminal apparatus is transmitted to a server apparatus and is aggregated for each GPS terminal apparatus. Then, a terminal apparatus connected to the server apparatus acquires the positional information regarding a target GPS terminal apparatus from the server apparatus and outputs to a display apparatus a map image and a position corresponding to the positional information on the map image. In the display apparatus, the position of the movable body is displayed time sequentially on the map image. Therefore, the user visually recognizes the present position and the moving locus of the child, the vehicle, or the like.
However, accuracy of the positional information deteriorates in a belowground shopping mall, in a building, in the shade of a building and the like, because radio waves received from a GPS satellite are weakened in such a place. Thus, there is a problem that calculated positional information represents an abnormal position where the movable body cannot exist. Therefore, a GPS terminal apparatus is known to take into account of a difference between calculated positional information and a true position in accordance with time information received from a GPS satellite, and is known to remove or putatively complement positional information which is estimated to be abnormal information including a significant difference.
Evaluation of difference is generally performed with presuming a model of a true value with respect to a measured value on the basis of assumption that a measured value “y” includes a difference “e” with respect to a true value “x”. It is possible to obtain a feasible model by examining a hypothesis of the model of a true value “x” that minimizes the difference “e” with respect to the measured value “y”. It is also possible to evaluate that the difference “e” is a difference between a value “x” corresponding to the obtained model and a measured value “y”. For example, i-th measured value “yi” in a plurality of measured values is expressed by yi=xi+ei. Then, a linear regression model is assumed, in which “xi” relative to time “t” is expressed by xi=a·ti+b. Regarding the assumed linear regression model, there is a method of calculating an estimated value of “xi” with defining coefficients “a” and “b” so as to minimize the sum of squares (expression 1) in a time distribution of the difference “ei”. In this case, the difference “ei” is evaluated by the difference between the measured value “yi” and the estimated value xi=a·ti+b.
                    (                  Equation          ⁢                                          ⁢          1                )                                                                                  ∑                          i              =              j                        k                    ⁢                      e            i            2                          =                              ∑                          i              =              j                        k                    ⁢                                    (                                                                    y                    i                                    -                  a                                ⁣                                                      ·                                          t                      i                                                        -                  b                                            )                        2                                              (        1        )            
Japanese Patent Application Laid-Open No. 2001-272466 discloses a technique wherein when the existence or position of a person or an object other than a vehicle is detected, a linear regression model relative to the measured value is assumed as described above, to thereby smoothen the difference, and putative difference with respect to an estimated position of the object continuously detected thereafter can be reduced.
In addition, it is known a method that is referred to as a Kalman filter for obtaining a statistical estimated value relative to a measured value (Japanese Patent Application Laid-Open No. 2002-6898). It is also known a method of correcting the position of a vehicle with using the Kalman filter in a car navigation system provided to a GPS.
Furthermore, it is disclosed a technique of effectively eliminating an impulse noise that is suddenly generated and using another measured value, with using a method referred to as a median filter in which neighboring measured values of interest measured value are sequentially arranged in a size order and a median value (median) is set as an estimated value (Japanese Patent Application Laid-Open No. 2006-270656).